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[1] Progrès en irrationalité (d'après C. Voisin, J.-L. Colliot-Thélène, B. Hassett, A. Kresch, A. Pirutka, Y. Tschinkel et al.), Séminaire Bourbaki, Institut Henri Poincaré, Paris (5th Novembre 2016) C. Voisin has invented a new method to prove that members of families of varieties are not stably rational, that is their product with an affine space is not rationnal. This method is based upon the decomposition of the diagonal in the Chow group and the specialisation properties of this decomposition. Among the new families concerned by this method are the double covers of the projective space of dimension tree or four ramified along a very general quartic hypersurface and quartic threefolds. These method also allow to construct a family of smooth varieties of dimension four for which the locus of rationality is neither open nor closed. | ||
